A recently developed method of making large earth-moving tires includes the sequential steps of wrapping layers of uncured rubber and wire around an annular core which remains within the tire carcass throughout the tire building process and is dissolved after the rubber is cured. The rubber and wire layers are applied in different types of work machines dependent upon the direction of the wrap. Thus, the core and the tire carcass in various stages of completion are handled several times. Once the core is made and the tire building process started, the core and tire carcass are maintained in a vertical direction. The weight of the core may exceed as much as 3,000 lbs. and the combined weight of the core and tire carcass of the larger sized tires may exceed 4,300 lbs. One of the difficulties encountered with such tire building process is the handling, transporting and precision positioning of the core, or the combined core and unfinished carcass, within the various work machines without damaging the somewhat fragile core or tire carcass before it is cured.